Definition:Jacobian Determinant/Also known as

Jacobian Determinant: Also known as

The Jacobian determinant is often called just the Jacobian of $\mathbf f$ at $\mathbf x$.

However, this can allow it to be confused with the Jacobian matrix, so it is advised to use the full name unless context establishes which is meant.

Some sources present this as $\map \det {J_f}$, but boldface for matrices is usual, and standard on $\mathsf{Pr} \infty \mathsf{fWiki}$.

Other sources present it as either $\mathbf J_{\mathbf f}$ or $J_f$, allowing a further source of confusion between this and the Jacobian matrix.